LCM of 144, 312, 688, 432, 964
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 144, 312, 688, 432, 964 with the LCM of Two or More Numbers Calculator. Here we are teaching you two different methods through which you can calculate the LCM of 144, 312, 688, 432, 964. So, keep reading to learn more.
Given numbers are 144,312,688,432,964
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 144,312,688,432,964 is 58198608.
Find LCM of 144,312,688,432,964 with Prime Factorization
| 2 | 144, 312, 688, 432, 964 |
| 2 | 72, 156, 344, 216, 482 |
| 2 | 36, 78, 172, 108, 241 |
| 2 | 18, 39, 86, 54, 241 |
| 3 | 9, 39, 43, 27, 241 |
| 3 | 3, 13, 43, 9, 241 |
| 1, 13, 43, 3, 241 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 2 x 2 x 3 x 3 x 1 x 13 x 43 x 3 x 241 = 58198608
Therefore, the lowest common multiple of 144,312,688,432,964 is 58198608.
LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
Firstly, we have to find the product of all the numbers.
144 x 312 x 688 x 432 x 964 = 12872600911872
Then, let us find the GCF of these five numbers. To do so, we have to list down the factors for each number and choose the highest factor that is in all of the lists.
144 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
688 : 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
432 : 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
964 : 1, 2, 4, 241, 482, 964
4 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 144,312,688,432,964, is 4.
Now, the common factors can be found like this.
144:2x 2x 2x 2x 3x 3
312:2x 2x 2x 3x 13
688:2x 2x 2x 2x 43
432:2x 2x 2x 2x 3x 3x 3
964:2x 2x 241
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 3x 3x 3 = 55296
Therefore, the value for common factors is 55296.
Now that we have all the elements of the formula, we can plug them in to calculate the LCM.
LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
LCM = 12872600911872/(4x55296)
LCM = 12872600911872/221184
LCM = 58198608
Thus, we can understand that the LCM of 144,312,688,432,964 is 58198608.
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FAQs on LCM of 144, 312, 688, 432, 964
1. What is the LCM of 144, 312, 688, 432, 964?
Answer: LCM of 144, 312, 688, 432, 964 is 58198608.
2. How to calculate the LCM of 144, 312, 688, 432, 964?
The LCM can be found using two methods. You can either use the LCM formula or the prime factorization method to calculate the LCM of 144, 312, 688, 432, 964.
3. What is the LCM formula?
The LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}.